In my DF game, I deliberately set up XP awards based on in-play accomplishments. Roleplaying is expected, not rewarded. Showing up is worth points only if you accomplish specific, tangible, in-game goals. There aren't any missions to accomplish - just looting and exploring - and you get XP based on how well you do those things.
In my previous GURPS game, I rewarded reaching certain, well, "plot points" for lack of a better word. Take as many sessions as you want to get there, but finish a mission or accomplish some goal and you'd get points. Plus, you'd get some minor points for just showing up. Half of those minor points if your PC was involved in danger despite you not being there - it wasn't a pick-up team like my DF game.
Those are far from the only ways to do it.
One other way is just flat rewards per session, assuming you don't just putz around doing nothing or nearly so.
That's how our Gamma Terra guys advance. We get 5/session, and every 5 sessions we get to roll on a table which has some random awards on it worth 2-20 points or so. Play five sessions and you're sure to get 25 points plus 2-20 more in a pre-selected advantage or skill. We're heavily driven by in-game goals we set ourselves, and overcoming the obstacles to those goals.
This guy here, Eric Crapo, is doing it in Pathfinder in the way they say you can in D&D5. It seems to be working for him as well.
It would be an interesting way to play DF in a megadungeon.
How could I do it?
Pick a fixed amount of XP. Say, 5/session. That's what we get in GT, and it would be the same as a good session of DF with our current system or our previous system.
Award that out based on each and every session, as long as you show up and make some kind of reasonable advancement towards exploration and "clearing" of the megadungeon. Find new stuff, figure out a puzzle, kill some significant foes, do some mapping that clarifies how things are (a variation of "find new stuff). Not just killing rats, knocking off an orc or two, or re-mapping a bunch of caverns because two connections don't seem to line up just right. But generally, do stuff, get your points.
You can adjust it by making it point-based, so low point characters earn more and higher point characters earn less, to get a "you learn more early" approach. Say, 10/session until 300 points, 5/session until 400, 2/session until 500, 1/session thereafter. This would parallel a "slower advancement as you level" or "you need more treasure for full XP" system.
That kind of adjustment would mean PCs have to make some early decisions about their approach, and really need to dig after any bonus points for MVP or accomplishing special goals (defeat an epic foe, find a hidden area, discover a new level, defeat a major curse, etc.) or just accept slow growth. Wizards would inevitably be more picky about spells, since they'd eventually run into an issue with "learn at least one new spell per downtime, plus one per level of Wild Talent with Retention" as they got up in points. Not really unfair, but that would be the word I'd expect to hear from nearly all players used to multiple points per session who run wizards.
Potential Impact on Play (in my game)
This would significantly change play. Right now, a treasure-and-exploration based system means you constantly need to push to find new areas, find rich monsters, kill off people with money (or get them to give it to you), and go deeper and deeper. As the session rolls on, desperation sets in if you aren't making that progress. Killing off former allies because you're broke or avoiding fights because they don't seem to come with money - and provoking them because they do - occur often with this system.
Conversely, it might drive players away from looting and the endless drive deeper. If the amount of money you take isn't significant, and rate of advancement is constant, you can ignore money except as your character needs it. It's purely a tool, not a goal.
It may potentially drive PCs stuck on a way forward to just basically mess around trying to tie up loose ends. If it's always X points per session, and it doesn't matter what you do, then you should just do some stuff you feel is doable. You don't necessarily need a long-term strategy.* It's better if you have one - no one likes to spend an entire game on level 1, just putting the time to get the points and it all leads somewhere - but it's not strictly necessary.
On the other hand, it means you can build towards long-term goals without worrying about this session. If you don't get loot this session, but set yourself up for a big payday later, that's fine. You might just grind down some foes, not finish them, but that's something you needed done. You can get distracted by unraveling a puzzle without worrying that "it better have loot behind it." And although I'd be surprised if this happens, it would mean you wouldn't need to tear off door fixtures, steal locks off of old chests, and pull apart tables for the nails to try to make a buck to make ends meet.
As a way of playing, there is nothing wrong with fixed advancement or advancement per session. It's just different, and I think it would have the impacts I spelled out above in my games. The "points no matter what" or "advancement every X sessions" approach, tossing out in-game fixed needs, potentially has a strong impact on play. Or no impact on play, in the case of our Gamma Terra game - we'd do what we were doing anyway, because we have goals to accomplish.
* In training terms, this is "go to the gym and do stuff for an hour" vs. "go and do your day's training that is part of an overall plan." My current XP system is the "train heavy or go home" and "if I'm not straining and sweating, it's not worth doing" approach, but fixed is potentially "each day builds on the next, no matter how hard or easy it seems" approach. Yes, I always think about training. And gaming. Often overlapping, although I don't do them together.